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Statistical Analysis and Hypothesis Testing: Regression, ANOVA, and Contingency Tables

Covers regression, ANOVA, and contingency tables.

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    Statistical Analysis and Hypothesis Testing: Regression, ANOVA, and Contingency Tables 1. Consider the following partially completed computer printout for a regression analysis where the dependent variable is the price of a personal computer and the independent variable is the size of the hard drive. Based on the information provided, what is the F statistic? About 8 .33 Just over 2.35 About 4.76 About 69.5 4 points Q U E S T I O N 2 1. The standard error of the estimate is a measure of total variation of the Y variable. the variation around the sample regression line. explained variation.

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    the variation of the X variable. 4 points Q U E S T I O N 3 3. Nintendo Sony would like to test the hypothesis that a difference exists in the average age of users of a Wii, a PlayStation, or an Xbox console game. The following data represent the age of a random sample of Wii, PlayStation, and Xbox users. Wii PlayStation Xbox 37 26 31 31 21 20 47 24 38 29 24 31 36 25 30 Using α = 0.05, the conclusion for this hypothesis test would be that because the test statistic is more than the critical value, we cannot conclude that there is a difference in the average age of users of a Wii, a PlayStation, or an Xbox console game. less than the critical value, we cannot conclude that there is a difference in the average age of users of a Wii, a PlayStation, or an Xbox console game. more than the critical value, we can conclude that there is a difference in the average age of users of a Wii, a PlayStation, or an Xbox console game. less than the critical value, we can conclude that there is a difference in the average age of users of a Wii, a PlayStation, or an Xbox console game. 4 points Q U E S T I O N 4

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    1. The relationship of Y to four other variables was established as Y = 12 + 3X1 - 5X2 + 7X3 + 2X4. When X1 increases 5 units and X2 In a sample of n = 23, the Student's t test statistic for a correlation of r = .500 would be: 2.559 2.819 2.646 can’t say without knowing α (alpha) 4 points Q U E S T I O N 5 1. Given the following ANOVA table (some information is missing), find the F statistic. 3.71 0.99 0.497 4.02 4 points Q U E S T I O N 6 1. Examine the following two - factor analysis of variance table:

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    Complete the analysis of variance table. MSA = 40.928, F Factor A =3.35, SSB = 85.35, Factor B df = 3, F Factor B = 2.316, MSAB = 21.859, F Factor AB = 1.8, SSE = 789.29, SSE df = 66, MSE = 12.143 MSA = 40.928, F Factor A = 3.35, SSB = 85.35, Factor B df = 4, F Factor B = 2.316, MSAB = 21.859, F Factor AB = 2.1 SSE = 789.29, SSE df = 66, MSE = 12.143 MSA = 40.698, F Factor A = 3.35, SSB = 84.35, Factor B df = 5, F Factor B = 2.316, MSAB = 21.859, F Factor AB = 2.1, SSE = 789.29, SSE df = 65, MSE = 12.143 MSA = 40.698, F Factor A = 3.35, SSB = 84.35, Factor B df = 3, F Factor B = 2.316, MSAB = 21.859, F Factor AB = 1.8, SSE = 789.29, SSE df = 65, MSE = 12.143 4 points Q U E S T I O N 7 1. The critical value for a two - tailed test of H0: ß1 = 0 at a (alpha) = .05 in a simple regression with 22 observations is: + or - 1.725 + or - 2.086 + or - 2.528 + or - 1.960 4 points

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    Q U E S T I O N 8 1. A regression equation that predicts the price of homes in thousands of dollars is t = 24.6 + 0.055x1 - 3.6x2, where x2 is a dummy variable that represents whether the house in on a busy street or not. Here x2 = 1 means the house is on a busy street and x2 = 0 means it is not. Based on this information, which of the following statements is true? On average, homes that are on busy streets are worth $3600 less than homes that are not on busy streets. On average, homes that are on busy streets are worth $3.6 less than homes that are not on busy streets. On average, homes that are on busy streets are worth $3600 more than homes that are not on busy streets. On average, homes that are on busy streets are worth $3.6 more than homes that are not on busy streets. 4 points Q U E S T I O N 9 1. The variation attributable to factors other than the relationship between the independent variables and the explained variable in a regression analysis is represented by regression sum of squares. error sum of squares. total sum of squares. regression mean squares. 4 points Q U E S T I O N 1 0 1. Degrees of freedom for the between - group variation in a one - factor ANOVA with n1 = 8, n2 = 5, n3 = 7, n4 = 9 would be: 28

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    3 29 4 4 points Q U E S T I O N 1 1 1. A hypothesis test is conducted at the 5 percent level of significance to test whether the population correlation is zero. If the sample consists of 25 observations and the correlation coefficient is 0.60, then the computed test statistic would be: 2.071 1.960 3.597 1.645 4 points Q U E S T I O N 1 2 1. A two - factor analysis of variance is conducted to test the effect that price and advertising have on sales of a particular brand of bottled water. Each week a combination of particular levels of price and advertising are used and the sales amount is recorded. The computer results are shown below. Based on the results above and a 0.05 level of significance, which of the following is correct? There is no interaction between price and advertising, so results for individual factors may be

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